HBM 511 - Scientific Computing I

Course Objectives

1. To provide sufficient mathematical background to understand the algorithms used in scientific computing.
2. To teach numerical algorithms for the problems arising from science and engineering which cannot be solved by exact methods.
3. To improve the student’s ability of writing, implementing and analyzing the numerical algorithms in various scientific programming languages.

Course Description

Introduction to number representation in computing systems. Taylor series expansion, floating-point representation and root finding. Direct Solutions of Linear Systems. LU and Cholesky factorization. Computational complexity, stability and conditioning. Nonlinear systems. Iterative methods for linear systems (Gauss, Seidel, Jacobi, SOR etc.). QR factorization and least squares. Eigen problems. Introduction to numerical methods for ordinary differential equations.